We report extensive measurements of quantum oscillations in the normal state of the Fe-based superconductor LaFePO, (T(c) approximately 6 K) using low temperature torque magnetometry and transport in high static magnetic fields (45 T). We find that the Fermi surface is in broad agreement with the band-structure calculations with the quasiparticle mass enhanced by a factor approximately 2. The quasi-two-dimensional Fermi surface consists of nearly nested electron and hole pockets, suggesting proximity to a spin or charge density wave instability.